Born Natalia Nikolaevna Zacharenko in San Francisco at the height of the Great Depression, Natalie Wood (“Natasha” to close friends) was one of those rare stars who managed to combine old-school glamor, powerhouse talent and smoldering sex appeal in a single package. Her drowning death off the California coast when she was just 43 years old remains one of Hollywood’s enduring mysteries, and the source of more than two decades’ worth of rumors, investigations and speculation.

Here, LIFE.com presents a selection of photographs made by Bill Ray in 1963 — a time in the 25-year-old Wood’s career when she had made the leap from actress to genuine movie star and, more importantly, to formidable Hollywood player.

[Many of the photos in this gallery were not originally published in LIFE, but appear in Bill Ray’s book, My Life in Photography. Buy the book here.]

For Bill Ray, the most striking memory of the several weeks that he spent with Wood and her showbiz cohorts is, unsurprisingly, Wood herself — or, more specifically, her singular beauty.

“She was divine,” Ray told LIFE.com. “Really. She was divine to look at, and to photograph. She had that wonderful face, a great body, those amazing eyes — just a beautiful young woman, and a lot of fun to be around.”

Ray, who was not yet on staff at LIFE, also recalls that this was a big — and for his career, perhaps pivotal — gig. At the time, LIFE published 51 issues a year, with a special double issue in late December. For the Dec. 20, 1963, issue that focused wholly on the movies, Ray scored the choice, high-profile feature on Wood — the only piece in the entire issue devoted to a single actor or actress. “This was big stuff,” he says today of the plum assignment. “You know, back then photographers were never part of the meetings where these sort of assignment decisions were made, so to get the call for something of this magnitude — I was thrilled.”

Thrilled, but hardly cowed or overawed. After all, by the time the Natalie Wood shoot came his way, Ray was a seasoned professional, having covered the likes of JFK, Elvis Presley, John Wayne and other huge names and famous faces. What comes through in so many of his photographs, meanwhile, is the sense that here was a photographer who genuinely enjoyed his work (and why wouldn’t he?), while his subject was a strong young woman who had been in the public eye for so long that having her every move documented was hardly anything new.

In fact, as LIFE reminded its readers in that special year-end double issue back in 1963, Natalie Wood was about as self-aware — and self-confident — an actress as one was ever likely to meet:

Natalie Wood was in a crowd watching a movie being filmed 21 years ago when the director asked her do a bit: drop an ice ream cone and cry. Then and there, 4-year-old Natalie showed she was born to be a star: she wept so convincingly that the movies hired her — and ever since they have been thankful for the foresight. . . . [Movies] still cannot get along without the glamor that stars bring. And Natalie, the biggest young star around, now holds Hollywood in her hand. Her latest performance in her 35th film, ‘Love With a Proper Stranger,’ may win her an Oscar. [Note: She did, in fact, earn an Academy Award nomination for the role, but Patricia Neal took home the Oscar that year for her work in ‘Hud.’] A 96-pound beauty in a size 5 dress, Natalie has talent which she uses brilliantly, temperament which she can control, and a dark fresh loveliness that glows from the screen. All this earns her a million dollars a year, along with something that means even more to her — the power and the glory that stardom brings.

“Natalie Wood,” observed a prominent Hollywood director, “is a powerful little broad who has a stranglehold on every young leading-lady part in town. If a role calls for a woman between 15 and 30, you automatically think of her.”

This is exactly what Natalie has worked 21 years to get. She has battled producers and top studio heads with unyielding ferocity to win the roles she wants. Today, before she will do a picture, she demands and gets total approval of script, director, leading man, all actors, everybody clear down to make-up and wardrobe people.

One last detail that Bill Ray recalls about his time with Natalie Wood, however, casts something of a pall across his otherwise sunny memories. At some point during those several weeks, he joined Wood and a number of other people on a boat ride to Catalina Island (see slide 16 in the gallery) — the same island off the California coast near which Wood would drown in the fall of 1981. When Ray heard about her death, he was stunned: not only because he had always liked her and remembered the time he spent with her with such fondness, but because he had been struck during that boat ride in 1963 by how uncharacteristically out of sorts she seemed.

“It was obvious to me,” Ray told LIFE.com, “that Natalie did not like being out on the water at all. When I heard that she’d drowned, in basically the same place where we’d been all those years before, I wasn’t just sad — although that was part of it. I was also very, very surprised.”

Five decades later, the mystery of Natalie Wood’s death endures. Bill Ray’s pictures, meanwhile, shed a clear, poignant light on a time when the star’s already impressive career felt boundless, and her life charmed. The future, it seemed then, was hers for the taking.